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Question

An isosceles trapezoid's top and bottom sides are marked by arrows. Its left and right sides are marked by 3 tick marks. The top base's angles are marked by 2 arcs. The bottom base's angles are marked by singular arcs.

Determine the degree of rotation that would turn the trapazoid onto itself.

Answer 1

To determine the degree of rotation that would turn the isosceles trapezoid onto itself, we first consider the properties of isosceles trapezoids. An isosceles trapezoid has two pairs of equal angles and two pairs of equal lengths (the non-parallel sides are of equal length).

1. Basic Properties:

   • The top base (parallel to the bottom base) is not equal to the bottom base in length but the sides connecting them (the legs) are equal.
   • The two angles adjacent to each base are equal (the ones at each top corner are equal to each other and the ones at each bottom corner are equal to each other).

2. Symmetry:

   • The isosceles trapezoid has a line of symmetry that is vertical (going down through the midpoints of the bases).
   • This symmetry indicates potential rotation points.

3. Rotation:

   • To determine the rotation that maps the trapezoid onto itself, we see that a 180-degree rotation about the vertical line of symmetry will map each point on the top base to the corresponding point on the bottom base and vice versa.
   • A 360-degree rotation would also leave it unchanged, but this is not the smallest rotation.

4. Conclusion:

   • The smallest angle of rotation that will allow the trapezoid to coincide with itself is 180 degrees.

Thus, the degree of rotation that would turn the isosceles trapezoid onto itself is 180 degrees.